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 his absolute motion with respect to the ether. In this way it was predicted that the time which would be required for a beam of light to pass a given distance and return would be different in the two cases when the path of light was parallel to the direction of motion and when it was perpendicular to the direction of motion.

But a classical experiment of Michelson and Morley, in which the ray-path was wholly in air, put this prediction to a crucial test; and not the slightest difference of time was found in the passage of light along the two paths. The extreme precision of their methods leaves no doubt as to the accuracy of the results.

In a similar manner the theory of a stationary ether gave rise to the prediction that a charged condenser suspended by a wire would exhibit a torsional effect due to the earth's motion. This prediction was tested in the crucial experiment of Trouton and Noble with the result of showing that no such torsional effect is present.

These results are in perfect agreement with the hypothesis that it is impossible to detect absolute translatory motion through space; and as a matter of fact they have been generalized into this hypothesis. A sharp formulation of this conclusion constitutes the first characteristic postulate of relativity.

Before stating the postulate, however, it will be necessary to introduce a definition. In order to be able to deal with such quantities as are involved in the measurement of motion, time, velocity, etc., it is necessary to have some system of reference with respect to which measurements can be made. Let us consider any set of things consisting of objects and any kind of physical quantities whatever each of which is at rest with reference to each of the others. Let us suppose that among these objects are clocks, to be used for measuring time, and rods or rules, to be used for measuring length. Such a set of objects and quantities, at rest relatively to each other, together with their units for measuring time and length, we shall call a system of reference. Throughout the paper we shall denote such a system by S. In case we have to deal at once with two or more systems of reference we shall denote them by $$S_{1},S_{2},\dots$$ Furthermore, it will be assumed that the units of any two systems $$S_1$$ and $$S_2$$ are such that the same numerical result will be obtained in measuring with the units of $$S_1$$ a quantity $$L_1$$ and with the units of $$S_2$$ a quantity $$L_1$$ when the relation of $$L_1$$ to $$S_1$$ is precisely the same as that of $$L_2$$ to $$S_2$$.